The ringtones were packed into an SMS message (or several, if it didn’t fit into one).
While SMS were designed to send text, nothing is really stopping someone from packing arbitrary data into one. The then-top companies-producers of mobile phones – Ericsson, Motorola, Siemens, Alcatel – came together with [EMS protocol](https://en.wikipedia.org/wiki/Enhanced_Messaging_Service), which allowed to transfer small files via SMS. If your phone supported EMS – it could extract ringtones from such special SMS. If it did not – it would just receive garbage mix of characters.
Later, MMS were developed, which used Internet to transfer data. It allowed sending pictures, videos, and music. It still used SMS to notify the phone that a new message have arrived, but the message itself were stored on a Web server.
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